Well.... They do kinda
Basically, if this formula is used, GCSEs are scored in context of the school's average performance - what was your school like?. They also may use a Merit Score, which is a way of standardising, or normalising, SUMS and GCSEs across all applicants.
There's also another document detailing correlation of different academic factors to Tripos performance
; from this, you can see that for Medicine, GCSEs are shown to have a stronger correlation than BMAT but weaker than AS UMS. I guess it's likely then that they will have some influence on intake, but it's hard to work out in what manner.
Also, there's a Powerpoint which shows scatter-plots of A*s at GCSE for Medicine applicants
; from this, you can see that the average nA*s is around 6 for applicants, yet around 8A*s for successful applicants (in this year). You can also see that no one got in with no A*s in this year
Also, this shows you the kind of UMS range the average successful applicant may have.
Basically... We can't know at this point if your ASs could redeem you, but with all Bs, they'd really have to be ****ing spectacular!
It may be that some colleges don't use GCSEs much, or that the viewing of GCSEs for Medicine has changed from when these articles were made, but you would be going up against hundreds of candidates with endless A*s and 95+% UMS, so being realistic, you may be cut-off before interview.
Really sorry if this seems harsh from me!